This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: lenoir (wml297) – homework 08 – Turner – (58220) 1 This printout should have 13 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 32 . 8 ◦ below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4 . 96 m / s 2 and travels 24 . 5 m to the edge of the cliff. The cliff is 23 . 5 m above the ocean. The acceleration of gravity is 9 . 8 m / s 2 . Find the car’s position relative to the base of the cliff when the car lands in the ocean. Correct answer: 19 . 5471 m. Explanation: Given : a = 4 . 96 m / s 2 , l = 24 . 5 m , h = 23 . 5 m , and θ = 32 . 8 ◦ . The speed of the car when it reaches the edge of the cliff is given by v 2 = v 2 i + 2 a l = 2 a l since v i = 0 m / s, so v = √ 2 a ℓ = radicalBig 2 (4 . 96 m / s 2 ) (24 . 5 m) = 15 . 5897 m / s . Now, consider the projectile phase of the car’s motion. The initial vertical velocity is v iy = v sin θ = (15 . 5897 m / s) sin(32 . 8 ◦ ) = 8 . 44509 m / s . and the vertical velocity with which the car strikes the water is v 2 y = v 2 iy + 2 g h = v 2 sin 2 θ + 2 g h = (15 . 5897 m / s) 2 sin 2 32 . 8 ◦ + 2 ( 9 . 8 m / s 2 ) (23 . 5 m) = 531 . 92 m 2 / s 2 , so that v y = radicalBig 531 . 92 m 2 / s 2 = 23 . 0634 m / s . To find the time of flight, v y = v iy + g Δ t Δ t = v y v iy g The initial horizontal velocity is v ix = v cos θ and the horizontal motion of the car during this time is x = v ix Δ t = ( v cos θ ) v y v iy g = (15 . 5897 m / s) cos 32 . 8 ◦ × (23 . 0634 m / s) (8 . 44509 m / s) (9 . 8 m / s 2 ) = 19 . 5471 m . 002 (part 2 of 2) 10.0 points Find the length of time the car is in the air. Correct answer: 1 . 49166 s. Explanation: Using the vertical motion, v y = v iy + g t t = v y v iy g = (23 . 0634 m / s) (8 . 44509 m / s) (9 . 8 m / s 2 ) = 1 . 49166 s ....
View
Full
Document
This note was uploaded on 04/15/2010 for the course PHY 12343 taught by Professor Turner during the Spring '10 term at University of Texas.
 Spring '10
 Turner

Click to edit the document details